Counting The Goats

G = goats, C = hens, L= total number of legs, and H = total number of heads

Given: L = 2H+14

Since goats have four legs and hens have two we can say L = 4G + 2C. We can also say that H = G + C since the number of heads is the sum of goats and hens. Substituting the right hand sides of these equations into the given equation gives us 4G + 2C = 2(G + C) + 14. Solving for G gives us G = 7.

let the number of goatsd be x, and number of hens be y. according to the question,the number of legs is 14 more than twice the number of heads i.e. 2(x+y)+14=2x+4y =>2x+2y+14=2x+4y =>2y=14 =>y=7

therefore, there are 7 goats in the shed...

Knowing that there are 2 legs on hens, and 4 legs on a goat, you can cancel out the number of hens, since you have "14 more legs than TWICE THE NUMBER OF HEADS". Therefore, you would simply have 2G * 14. Simplify, and you have a quotient of 7, the number of goats.

In this method, it doesn't matter how many hens there are.

let the total no. of goats and hens be X and Y respectively total no. of legs of goats= 4X total no. of legs of hen = 2Y According to the question 4X+2Y=2(X+Y)+14 =2(2X+Y)=2(X+Y+7) = 2X+Y=X+Y+7 = X=7 therefore total no. of goats = 7

X= No of hens, Y = No of goats.

No of legs = 2(No of heads) + 14.

Since Goat has 4 legs and hen has 2 Legs.

2X + 4Y = 2(X + Y) + 14.

Now Simplifying the above equation, we get 2Y = 14.

Dividing by 2, will get no of Goats. which is 7.

goat has 4 legs and 1 head hen has two legs and 1 head

So then there are zero hens?

Total number of legs: 2(C+G) + 14 = 4G + 2C G = 7

My solution was to go about it by turning the information given straight into an equation. So firstly make sure to make a mental note that goats have 4 legs and hens have 2 legs as this is easy to forget. Then write it as an equation in the form:

14=(4X+2Y)-2(X+Y)

In this equation X=1 goat head and Y=1 hen head. For number of legs just times the value by how many legs the animal has, thus, you will use values 4X and 2Y. If you add these together you have total number of legs. Next you just need to take away 2(X+Y) from this value for it to equal 14. So now that the information has been re-wrote in the form of an equation it just needs to be expanded and rearranged to find the number of goats.

Expanded: 14=4X+2Y-2X-2Y

Simplified: 14=2X

Solution: X=7

Hens have 2 legs and goats have 4 legs. All of the animals have at least two legs. When it says that the number of legs are 14 more than twice the number of heads, the number of legs minus 14 divided by two is equal to the number of animals. multiply it by two, and you get the number of animals with at least two legs. It says 14 more, which means that if you divide 14 by two , you get 7 pairs of two legs, added to the previous two legged animals, you get the four legged animals, goats. BAM - 7 goats.

Let hg = goat head __ L = legs

    hn = hen head             __          H = Heads

Legs = 14 + 2 x Heads ---------(1)

but

legs = 4 x hg + 2 x hn--------(2)

heads = hg + hn--------------(3)

substituting 2 & 3 in eq. 1

we get

4hg + 2hk = 14 + 2hg + 2hk

2hg = 14

hg = 7

number of heads=x number of legs = 14 +2x numbre of goats + number of hens = x number of goats = x ــ number of hens the goat has 4 legs the hen has 2 legs 4(number of goats)+2(number of hens ) = number of legs = 14 +2x 4(x ــ number of hens)+2(number of hens )=14 +2x 4x (- 4) ( number of hens)+2(number of hens )=14 +2x 4x (-2)(number of hens)=14 +2x (-2)(number of hens ) = 14 -2x number of hens = -7+x so, number of goats = x ــ number of hens = x-(-7+x)=7

Simply , let L=2l ,and H where H=the total number of heads. L= is the total number of legs and l= is the total number of legs in pairs

then the given eguation L=2H+14 becoms 2l=2H+14 by dividing by 2 l=H+7 by consedring that all animals in the shed are hens then we have a head for each two legs (this are normal hens :) and 7 pairs of legs without heads and this are not normal hens but idicating to 7 pairs of back legs of goats so we have 7 goats in the shed not depending on algebra all the time :D

number of heads=x number of legs = 14 +2x numbre of goats + number of hens = x number of goats = x ــ number of hens the goat has 4 legs the hen has 2 legs 4(number of goats)+2(number of hens ) = number of legs = 14 +2x 4(x ــ number of hens)+2(number of hens )=14 +2x 4x (- 4) ( number of hens)+2(number of hens )=14 +2x 4x (-2)(number of hens)=14 +2x (-2)(number of hens ) = 14 -2x number of hens = -7+x so, number of goats = x ــ number of hens = x-(-7+x)=7

x=nos of head ; y=nos of legs which is four 2x+14=4y (y=x) 2x=14 ;x=7

goats times two plus hens times two is the number of heads times two

the number of legs is goats times two plus hens times two

the difference between those is goats times two

that means that the goats times two is 14

14 divided by two is seven

let x be the number of goats y be hens then 2(x+y)+14=4 x+2 y ,2 x+2 y+14=4 x+2 y,4 x-2 x+2 y-2 y=14,2 x=14,x=7 so number of goats=7

let x be the number of goats and y be the number of hens. From the equation, no. of legs= 14+2(no.of heads) =>4x+2y=14+2(x+y) Solving the above equation,we get x(the no of goats)=7

I just did this let x be the number of heads so 2x+14 = 0

2x=-14 x=-7 since there is no negative in animals so the answer is 7

We know that:

if Head is b and every creature got head, goats are x, hens are y, because goats got 4 leg and hens got 2 leg so:

$Leg=4x+2y$

$Leg=2b+14$

$Head=b=x+y$

* Do the magic:

Subtitude b to Leg

$Leg=2(x+y)+14=2x+4y$

$2(x+y+7)=2(x+2y)$

$x+y+7=x+2y$

$7=x+2y-(x+y)=x+2y-x-y$

$7=y=goats$

You just read and Think positive!

i solved it in this way

x=nos of head ; y=nos of legs which is four 2x+14=4y (y=x) 2x=14 ;x=7

let suppose total no of goats = x total no of hens= y we know that a goat has four legs and a hens has two legs so total no of legs = (4x+2Y) total no of heads = (x+Y) According to question 4x+2y = 2(x+y)=14 2x =14 hence x =7

we take goat as g, and the hen h. From the question we get this equation nr of legs 4g+2h=2(g+h)+14 we solve it and we get from there nr of g=7 so there are 7 goats. *in albanian : Goat= dhi/cjap

Create the variables { $g$ =number of goats, $c$ =number of hens}.

Goats have 4 legs and hens have 2, so the total number of legs is equal to $4g+2c$ . The number of heads would be equal to $g+c$ , since both animals have one head.

1. With these values, we can create the equation $4g+2c=14+2(g+c)$ , or $4g+2c=14+2g+2c$ based off of what the problem says. The second equation was created through the distributive property of equality.

2. If we subtract $2c$ from both sides, we get the equation $4g=14+2g$ .

3. Now we can subtract $2g$ from both sides to get $2g=14$ .

4. All we have to do is divide both sides by two, and we will have achieved the result $g=7$ while abiding by SADMEG.

Since whatever $g$ is equal to will be the answer, we now know that 7 is the number of goats!